https://doi.org/10.1140/epjp/s13360-024-04971-0
Regular Article
Exploring the rich solution landscape of the generalized Kawahara equation: insights from analytical techniques
1
School of Medical Informatics and Engineering, Xuzhou Medical University, 209 Tongshan Road, 221004, Xuzhou, Jiangsu Province, People’s Republic of China
2
Department of Basic Science, Obour High Institute for Engineering and Technology, 11828, Cairo, Egypt
a mostafa.khater2024@yahoo.com, Mostafa.khater2024@xzhmu.edu.cn
Received:
16
May
2023
Accepted:
1
February
2024
Published online:
23
February
2024
The primary objective of this investigation revolves around scrutinizing the generalized Kawahara equation, a consequential nonlinear evolution equation prevalent in diverse physical domains such as shallow water waves, ion-acoustic waves within plasmas, and nonlinear acoustics. This equation manifests intricate dynamical attributes, notably featuring the emergence of solitary waves, shock waves, and chaotic solutions. In our pursuit to elucidate the nuanced behavior inherent in the generalized Kawahara equation, we deploy two robust analytical methodologies: the Khater II method and the variational iteration method. These methodologies offer adept and precise avenues for approximating solutions to nonlinear partial differential equations. Through our analytical scrutiny, a diverse spectrum of solutions comes to light, encompassing solitary wave solutions, periodic solutions, and chaotic solutions. Our exploration delves into the impact wielded by diverse parameters on solution behaviors, thereby furnishing invaluable insights into the foundational physical mechanisms at play. The findings derived from our inquiry contribute significantly to comprehending the intricate dynamics of the generalized Kawahara equation, concurrently establishing connections with other nonlinear evolution equations. This study augments the existing reservoir of knowledge concerning nonlinear wave phenomena and sets the stage for further investigations into the convoluted behaviors exhibited by these intricate systems.
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© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2024. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
